EC202 SIGNALS & SYSTEMS PREVIOUS QUESTION PAPER

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Reg. No.______________ Name:______________________
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017
Course Code: EC202
Course Name: SIGNALS & SYSTEMS
Max. Marks: 100 Duration: 3 Hours
PART A
Question No. 3 is compulsory.
1. a) Plot the signal ( ) = ( + 1) + 2 ( ) − ( − 3) − 2 ( − 5) (4)
b) Check the periodicity of given signals. Find the fundamental period if periodic
i) x(t) = 10 sin 25 πt + cos 10 πt
ii) ( ) = cos − sin + 3 cos + (4)
c) Determine whether the following system is time invarient, linear and causal.
( ) = ( ) + ( )
(5)
d) Evaluate the following integral ∫ cos (πt) δ(2t – 10)dt (2)
OR
2. a) What is the output sequence of a LTI system with impulse response h(n)=[3 , 2] to the
input x(n)=[1, 2,3, 3]? (5)
b) Compute the auto correlation of the signal x(n) = anu(n) for 0< a < 1 (6)
c) Check the causality and stability of the systems whose impulse responses are given
i) ℎ( ) = ( )ii) ℎ( ) = 2 (− ) (4)
(a < 0)
3. a) Find the output of an LTI system whose impulse response is h(t) to the input x(t).
ℎ( ) = ( ) − ( − 1)
x(t)=
t
2
-2
1
2

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(8)
b) For the given signal, plot x(3-3t)
1
(3)
c) Classify the following signals into energy, power or neither. Determine energy and
power.
i) (− ) ii) | |
(4)
PART B
Question No. 6 is compulsory.
4. a) Determine the Fourier series representation of the signal shown in figure.
(8)
b) Compute and sketch the magnitude and phase spectrum of the signals
i) ( ) = | |
(a>0) (4)
ii) x(t) = cos2 (2πt + 5) + 2sin (5πt) (3)
OR
6-6 -3 3 t
x(t)

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5. a) The step response of an LTI system is by (1 − − ) ( ). For an input ( ), the
output is observed to be (2 − 3 + ) ( ). For this observed measurement,
determine the input to the system using laplace transform. (6)
b) State the sampling theorem for low pass signals (2)
c) Determine the Nyquist rate of sampling for the signals
i) x(t) = 2sin 250πt + 3cos2
500t (2)
ii) x(t) = 10 sinc 500t (3)
d) A signal x(t) = 2 cos 400πt + 6 cos 600 πt is sampled with a sampling frequency
800Hz. Write the resultant discrete time signal. (2)
6. a) Find the Fourier Transform of following signals x1(t) and x2(t)
(Any relevant property can be applied) (10)
b) A continuous time LTI system is described by the differential equation
( ) + 5 ( ) = ( )
Determine the response of the system to the input ( ) = ( ) using Fourier
Transform. (5)
PART C
Question 9 is compulsory.
7. a) Evaluate the inverse Z-transform of
( ) = log |a|<|z| (4)
b) Evaluate the DTFT of following signals
i) x(n) = an sin Ω0 nu(n) (4)
4
-4
A
-A
x2(t)
t
5
T 2T t
x1(t)
0

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ii) x(n) = 0.25n u(n+2) (4)
c) Give the Parseval’s theorem for DTFT. Prove it. (4)
d) Compute the energy of the sequence ( ) =
Ω
(4)
OR
8. a) A system is described by the difference equation
( ) = ( ) − ( − 1) −
1
4
( − 1) +
1
8
( − 2)
Determine the impulse response of the system using fourier transform. Also find the step
response of the system. (8)
b) An LTI system is characterized by the system function given as
( ) =
3 − 4
1 − 3.5 + 1.5
Under what conditions the system will be obey causality and stability? (4)
Determine the impulse response of the system such that
i)The system is causal ii) The system is stable
Justify the answers. (8)
9. a) The frequency response of a three point moving average system is given as
Ω
= (1 + cos Ω) Ω
. Determine the difference equation representation
of the system. (5)
b) Determine the response of the system with impulse response ℎ( ) = (0.5) ( ) to
the input signal ( ) = 10 − 5 sin (5)
c) Find the z-transform and specify ROC
i) ( ) = ( − 2) ∗ ( ) ( ) (* stands for convolution) (5)
ii) ( ) = − ( ) (− − 1) (5)
***